A light-section based semi-ordered point cloud three-dimensional reconstruction method

Abstract

The application discloses a kind of three-dimensional reconstruction methods for light-cut type based on semi-ordered point cloud, comprising: step 1: define point cloud format;Step 2: select target object for scanning, obtain semi-ordered point cloud;Step 3: analyze the error source of measurement data;Step 4: detect and extract the hole boundary in point cloud model;Step 5: based on bayesian model, the hole of point cloud is repaired.The application is based on the classic structured light triangulation method, obtains semi-ordered point cloud, has the flexibility of discrete point cloud, also has the regularity of ordered point cloud, is very suitable for high-precision three-dimensional reconstruction.According to semi-ordered point cloud, by establishing bayesian probability model in hole area, the maximum likelihood parameter estimation is carried out to the region to be grown in combination with the specific distribution of point cloud, can maximize the comprehensive consideration of local features and global optimization.

Description

Technical Field

[0001] This invention relates to the field of 3D reconstruction technology, and in particular to a 3D reconstruction method based on semi-ordered point clouds for optical sectioning. Background Technology

[0002] 3D reconstruction technology has broad application prospects in fields such as industry, construction, biomedicine, transportation, aerospace, and military. Accurate acquisition of digital point clouds is a crucial step in 3D reconstruction. Optical active non-contact 3D point cloud acquisition methods are often used for high-precision reconstruction of complex targets due to their high measurement accuracy and large amount of effective information. Currently, various 3D laser scanners are commonly used. The Time-of-Flight (TOF) method relies on time resolution, has high requirements for equipment parameters, is expensive, and is difficult to adapt to complex environments. Optical interferometry methods (such as the moiré fringe method) mainly depend on the size of the reference grating, cannot reconstruct larger objects, and have poor measurement stability. Phase measurement profilometry (also known as grating projection) has a small measurement range, strict measurement environment requirements, and is difficult to promote in practical applications. Structured light triangulation, as a non-contact high-precision measurement method, retains the advantages of wear-free operation, high efficiency, high accuracy, and low cost, while also exhibiting stronger environmental adaptability, higher measurement robustness, and wider application scenarios. Its measurement accuracy can reach the micrometer level, thus attracting considerable attention.

[0003] Traditional structured light triangulation combined with a mature algorithm for extracting the centerline of light stripes can obtain the coordinate information of the target contour within the current light plane. With the aid of a third-degree-of-freedom motion device, complete 3D information of the currently covered scene can be obtained. When measuring the offset information of each cross-sectional layer, if the target is rigid or static, it can be converted into displacement. The accuracy of the point cloud obtained in this way is largely affected by the parameters and performance of the light triangulation system and the motion device. When the target is non-rigid or dynamic, the information obtained by the above method between adjacent frames does not have strong spatial correlation, and the results obtained by directly fitting the data have low confidence and are insufficient for high-precision 3D reconstruction of such scenes.

[0004] Furthermore, in a single-frame structured light imaging scenario, the stripes have a certain thickness, and the two-dimensional image encompasses information from multiple dimensions, such as the light intensity distribution in a certain direction, the normal information of the boundary equation, and the probability density function information of gray values. If, as described in traditional methods, information about a certain depth coordinate is obtained solely through mapping the centerline, the information utilization is extremely low, and it is difficult to establish topological information within a local region with high confidence.

[0005] In practical applications of point clouds, due to self-occlusion caused by the complex and multi-part structure of the target to be reconstructed, noise introduced by the measurement environment and the surface characteristics of the target object, or inherent limitations such as incomplete scanning / dead zones and data loss of the front-end equipment, the point cloud often exhibits a hole phenomenon caused by missing data. These holes cause the polygonal mesh obtained from real-world objects to exhibit defects that do not meet algorithm design standards, such as degenerate elements, self-intersecting / overlapping parts, and surface holes, limiting the application scenarios of point clouds. In addition, the original point cloud acquired in dynamic scenes may also exhibit a hole phenomenon caused by missing data due to the high relative speed of the target object, the limited function or parameters of the acquisition equipment, and the complexity of the scene composition, which in turn affects the accuracy, uniformity, and effectiveness of the point cloud and cannot meet the requirements of subsequent point cloud processing algorithms such as modeling. At the same time, when the point cloud model is subjected to large-scale deformation, cracks and other phenomena may also appear in the model.

[0006] Various classic point cloud hole repair algorithms exist for discrete point clouds, but these algorithms have some drawbacks. On the one hand, some algorithms focus on universality, transforming the hole repair problem into a surface closure problem. While this makes the algorithm more efficient and robust, and the repair results feasible and controllable, it also results in the loss of local detailed features, thereby reducing the overall fidelity of the data and the quality of the point cloud. On the other hand, other algorithms focus more on processing the detailed features of the point cloud, pursuing the restoration of missing data with higher confidence. This operation can sometimes introduce errors such as disordered topology or self-intersecting surfaces, requiring adaptive adjustments to algorithm parameters or human intervention. Furthermore, the goals and implementation methods pursued by these algorithms are not entirely suitable for semi-ordered point clouds, a target whose dimension lies between scattered and ordered point clouds.

[0007] Therefore, this invention proposes a 3D reconstruction method based on semi-ordered point clouds for optically tangential structures. Building upon the classic structured light triangulation method, it acquires semi-ordered point clouds, possessing both the flexibility of discrete point clouds and the regularity of ordered point clouds, making it highly suitable for high-precision 3D reconstruction. Furthermore, for semi-ordered point clouds, a Bayesian probability model is established in the hole region, and maximum likelihood parameter estimation is performed on the region to be grown, taking into account the specific distribution of the point cloud. This allows for a comprehensive consideration of both local features and global optimization. Summary of the Invention

[0008] To achieve the above objectives, this invention provides a method for 3D reconstruction based on semi-ordered point clouds using optical sectioning, comprising:

[0009] Step 1: Define the point cloud format as follows:

[0010]

[0011] x i ,yi ,z i Belongs to the inner p of point cloud i Three-dimensional coordinate information of a point; n i p i Normal information of a point on the current frame plane; p i Normal information between the point and its two nearest points on the current movement axis; I i p i Light intensity information of a point; ID represents p i The discrete attribute category to which the point belongs;

[0012] Step 2: Select the target object and scan it to obtain a semi-ordered point cloud;

[0013] Step 3: Analyze the sources of error in the measurement data;

[0014] Step 4: Detect and extract hole boundaries in the point cloud model;

[0015] Step 5: Repair the holes in the point cloud based on the Bayesian model.

[0016] Further, step 2 includes:

[0017] Based on the structured light triangulation method, normal vector information and light intensity information in light stripes are added to the discrete point cloud. When the offset of each cross section layer can satisfy that the vector information covered by the laser stripes of two adjacent frames is not parallel on the current extension line, a spatiotemporal field model can be established in the thickness light stripe. The topological structure information under the preset confidence level can be established in the unified world coordinate system, thereby obtaining the semi-ordered point cloud with a dimension between discrete point cloud and ordered point cloud.

[0018] Furthermore, the sources of error in step 3 include: random errors introduced by structured light width, collimation, and drift; systematic errors introduced during the construction of the optical cutting system; and random errors introduced by various types of noise in the measurement environment.

[0019] Furthermore, the optical cutting system is calibrated using a cross-point algorithm.

[0020] Further, step 4 includes:

[0021] Step 4.1: Select a point p in the semi-ordered point cloud. i Search and generate its neighborhood point set T(p) in the point cloud model;

[0022] Step 4.2: Calculate point p i Given the covariance matrix, find the eigenvectors corresponding to its smallest eigenvalues ​​and the normal vector of the tangent plane;

[0023] Step 4.3: Project T(p) onto the unit circle of the tangent plane to obtain the set of mapped points T′(p);

[0024] Step 4.4: Determine the value of point p i Is it a point to be determined?

[0025] Step 4.5: Determine the value of point p based on the prior information in the point cloud model. i If a point is a boundary point of a hole, it will be removed if it does not meet the requirements.

[0026] Step 4.6: Return to Step 4.1 until all points to be determined have been looped;

[0027] Step 4.7: Verify whether there are other boundary points in the neighborhood of each hole boundary point, and determine whether they are false boundary points.

[0028] Further, step 4.4 includes:

[0029] Calculate the maximum angle θ between each point in the mapping point set T′(p) and the points on the left and right sides. i Let θ max =max{θ i};If θ max If the value is greater than the judgment threshold, then point p... i The point is to be determined; otherwise, the point p is to be determined. i Let be an interior point.

[0030] Further, step 5 includes:

[0031] Step 5.1: Set the set of true values ​​O and the set of measured values ​​M for the target or scene to be reconstructed, wherein the set of measured values ​​M is generated by the set of true values ​​O and includes statistical error, and its descriptive model is P(M|O);

[0032] Step 5.2: Assuming the measurement process is an unbiased estimation, and describing the measurement process using statistical concepts under Bayes' theorem, the probability that the reconstructed set after being given the set of measured values ​​M is exactly the true set O is:

[0033]

[0034] Step 5.3: Determine the set O corresponding to the case where P(O|M) is maximized:

[0035]

[0036] Step 5.4: Determine the point cloud obtained during a particular measurement process. In this context, each of the m points is mapped to a point in the set of measured values ​​M.

[0037]

[0038] Among them, measurement point m i It is from the original point o i Accompanying probability density p i (o i It is caused by the measurement error of +Δx);

[0039] Step 5.5: The errors in the optical sectioning system are predominantly Gaussian distributed, and the errors are independent of each other. (Reconstruction points...) Conforms to p i (m i -Δx):

[0040]

[0041] Step 5.6: Define the prior set as consisting of density priors, Riemannian manifold priors, and discrete attribute feature priors, which are independent of each other.

[0042]

[0043] Where Z is a normalization constant representing the integral of all other factors in the set; w(O) is a window function that defines the area to be repaired in the point cloud model and makes the objective function integrable.

[0044] Furthermore, the density prior is defined as follows:

[0045] Define a non-uniformly probable random potential p within the defined region. dist This indicates that within a proportional neighborhood radius, the probability density has a local maximum at the desired point:

[0046]

[0047] Where, N δ (x) represents the set of all points contained in set O within the radius δ of point x; the radius δ is calculated iteratively from the expansion region of the hole to be repaired; N increases positively correlated with the singularity of the original point cloud model.

[0048] Furthermore, the Riemannian manifold prior is defined as follows:

[0049] The problem of the distribution of the original point cloud is transformed into an unconstrained optimization problem of the sum of several component functions on a Riemannian manifold:

[0050]

[0051] Here, L is a complete Riemannian manifold, and the function fi is a convex function defined on L;

[0052] Define T pL is the tangent space of the manifold L at point p, and TL = ∪ p∈M T p Let L denote the tangent bundle of the manifold L, and let χ(L) denote the vector field space on the manifold L; then the following derived definition holds:

[0053] (1) Define a T for each p∈L p The inner product g(p) on L = <,·> p Then g = {<·,·>} p} p∈L ={g(p)} p∈L Let (L, g) be a Riemannian metric on the manifold L, and g ∈ T. 0,2 L is a second-order covariant tensor field;

[0054] (2) Let Let γ:[a,b]→L be a smooth curve in the Riemannian manifold (L,g), and let L be a Levi-Civita connection on the Riemannian manifold (L,g). The geodesic curvature vector is called γ, where γ′(t) represents the derivative of γ at t; if The curve γ is then called a geodesic in the manifold L;

[0055] (3) If (L,g) is a smooth Riemannian manifold, given p∈L, v∈T p L, then there exists a unique geodesic γ v [a,b]→L makes γ v (a) = p and γ′ v (a) = v; where, when γ:[a,b]→L is a geodesic, ‖γ′‖ is a constant; γ is a normal geodesic if and only if ‖γ′‖ = 1;

[0056] The corresponding incremental subgradient algorithm on the Riemannian manifold is as follows:

[0057] a) Choose any point x0∈L, and let k=0;

[0058] b) Perform an optimization test on the objective function: if Then stop iterating; otherwise, let ψ 0,k =x k If i = 1, proceed to the next step;

[0059] Satisfy α k A sequence of points >0;

[0060] e) Following steps c) and d) above, repeat the calculation until i = m, and then calculate ψ. m,k Let it equal x k+1 ;

[0061] Let k = k + 1, and return to step b) to perform the optimization test.

[0062] Furthermore, the prior definition of the discrete attribute features is:

[0063] Determine whether a point belongs to the type of region, boundary, or corner point, where the region is defined as a smoothly connected surface, the boundary is defined as the boundary line between surfaces, and the corner point is defined as the intersection of n ≥ 2 boundaries; where...

[0064] (1) The point cloud model includes a neighboring region within a certain radius, including the discrete feature points mentioned above, which is called a special region;

[0065] (2) The point cloud model is divided into independent and uncoupled smooth regions by each boundary line, and the region does not contain discrete feature points, which is called a normal region; the boundary points belong to two adjacent regions.

[0066] (3) In the special region: the probability of the boundary increases with the curvature of the local neighborhood; the probability of the corner point depends on the number of boundary intersections in the neighborhood;

[0067] (4) The corner point can only exist in a certain radius neighborhood where two or more boundary lines intersect, and its probability distribution should satisfy the regression line after each boundary line is optimized to be the same.

[0068] (5) The neighborhood defined in the density prior and the Riemannian manifold prior is restricted to the same neighborhood in this process, and no additional attributes are divided.

[0069] Compared to existing technologies, the advantages of this invention are as follows: It proposes for the first time a Bayesian hole repair algorithm for semi-ordered point clouds, which exhibits a series of advantages in detail / structure preservation, robustness, accuracy, and robustness. In particular, by leveraging the characteristics of semi-ordered point clouds, it utilizes existing parameters as much as possible during hole boundary detection and prior knowledge optimization, significantly reducing inefficient computational processes common in similar methods. Furthermore, it eliminates concerns about topological definition errors and self-intersection confusion introduced by complex processing procedures. In addition, the introduction of three types of prior functions ensures the algorithm's feasibility and controllability in general environments and comprehensively considers the combination of global optimization and local features, further improving the algorithm's fault tolerance, noise tolerance, and the high structural quality of the repaired results.

[0070] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0071] Figure 1 This is a structural diagram of the high-precision optical cutting system of the present invention;

[0072] Figure 2 This is the result of the actual measurement of point cloud holes and algorithm repair of 3D printed rabbit ears according to the present invention;

[0073] Figure 3 This is a flowchart illustrating the algorithm principle of this invention. Detailed Implementation

[0074] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0075] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0076] This invention provides a 3D reconstruction method based on semi-ordered point clouds for optical sectional analysis. It acquires semi-ordered point clouds and then applies a Bayesian hole repair algorithm to them. Building upon the classic structured light triangulation method, high-dimensional information such as normal vectors and light intensity information from the light stripes is added to the discrete point cloud. When the offset of each layer of cross-sections satisfies the requirement that the vector information covered by the laser stripes in two adjacent frames is not parallel along the current extension line, a spatiotemporal field model is established in the thickness of the light stripes. This allows for the establishment of topological structure information with a pre-set confidence level within a unified world coordinate system, resulting in a semi-ordered point cloud with a dimension between that of a classic discrete point cloud and an ordered point cloud. The spatiotemporal field model includes coupling time and spatial parameters, such as normal vectors, sampling time, probability density distribution functions, and grayscale distribution, within two adjacent frames of data, making the two frames non-independent. Generally, any system of conditions established along a coordinate axis can be considered semi-ordered. For confidence levels, a confidence level of 0 corresponds to a discrete point cloud, a confidence level of 1 corresponds to an ordered point cloud, and a confidence level in between corresponds to a semi-ordered point cloud. Semi-ordered point clouds possess both the flexibility of discrete point clouds and the regularity of ordered point clouds, making them highly suitable for high-precision 3D reconstruction. These semi-ordered point clouds can provide a unique set of normal vectors along a specific axis, as well as other higher-dimensional information, improving information utilization and confidence. The semi-ordered point clouds acquired by the optical sectioning system can provide a unique set of normal vectors along a specific axis, as well as other higher-dimensional information. For semi-ordered point clouds, a Bayesian probability model is established in the hole region, and maximum likelihood parameter estimation is performed on the region to be grown, combined with the specific distribution of the point cloud. The core is to leverage the Bayesian probability model, supplemented by targeted prior knowledge of density, Riemannian manifold, and discrete attributes, to maximize the comprehensive consideration of local features and global optimization.

[0077] like Figure 1 As shown, the three-dimensional reconstruction method of this invention is implemented based on an optical sectioning system. The main components of the optical sectioning system include a laser light source (line or surface), a triangulation system, and a scanning mechanism. The movement mode of the optical sectioning system can be adjusted according to the application scenario, such as translation, rotation, pitch scanning, or a combination of multiple degrees of freedom. Preferably, the laser light source can be an OSELA SL-660-130-RS-A-60 line structured light source, the triangulation system can be a DAHENG IMAGING MARS-1230-23U3C camera or a Computar V1228-MPY2 lens, and the scanning mechanism can be a Guangzhou Hengyang Electronics Technology Co., Ltd. LDY-3-300 one-axis motorized translation stage.

[0078] The three-dimensional reconstruction method of the present invention includes the following steps:

[0079] Step 1: Define the point cloud format as follows:

[0080]

[0081] x i ,y i ,z i Belongs to the inner p of point cloud i Three-dimensional coordinate information of a point; n i p i Normal information of a point on the current frame plane; p i Normal information between the point and its two nearest points on the current movement axis; I i p i Light intensity information of a point; ID represents p i The discrete attribute category to which a point belongs. The target being measured is diverse. When it is a static / rigid / simple target, discrete attributes such as boundaries, coupling edges, corners, and vertices can be intuitively defined. However, when it is a dynamic / non-rigid / complex target, the definition of discrete attributes depends on the high-dimensional features of the point cloud data; the dimension is variable and not limited to a specific representation.

[0082] Step 2: Select the target object and scan it to obtain a semi-ordered point cloud;

[0083] Step 3: Analyze the sources of error in the measurement data: a) random errors introduced by characteristics such as structured light width, collimation, and drift; b) systematic errors introduced during the construction of the optical cutting system (variations in dynamic or static parameters); c) random errors introduced by various noises in the measurement environment. Therefore, the system uses the crosspoint algorithm for calibration, and its measurement accuracy is verified to be 28 μm using a 0-level gauge block. The crosspoint algorithm can be the one described in Chinese Patent Publication Document CN110470239A.

[0084] Step 4: Detect and extract hole boundaries in the semi-ordered point cloud model;

[0085] Step 5: Repair the holes in the point cloud based on the Bayesian model.

[0086] Furthermore, such as Figure 2 and Figure 3 As shown, step 4 specifically includes:

[0087] Step 4.1: Select a point p in the point cloud. i Search for and generate its neighborhood point set T(p) in the model;

[0088] Step 4.2: Calculate point p i Given the covariance matrix, find the eigenvectors corresponding to its smallest eigenvalues ​​and the normal vector of the tangent plane;

[0089] Step 4.3: Project T(p) onto the unit circle of the tangent plane to obtain the set of mapped points T′(p);

[0090] Step 4.4: Determine the value of point p i Is it a point to be determined, or an interior point?

[0091] Calculate the maximum angle θ between each point in T′(p) and the points on the left and right sides. i Let θ max =max{θ i}. If θ max If p is greater than the judgment threshold, then i p is a point to be determined; otherwise, p i Let it be an interior point;

[0092] Step 4.5: Determine p based on the prior information in the point cloud model (based on shape, breakpoints, sampling space, etc.). i If a point is a boundary point of a hole, it will be removed if it does not meet the requirements.

[0093] Step 4.6: Return to Step 4.1 until all points to be determined have been looped;

[0094] Step 4.7: Verify whether there are other boundary points in the neighborhood of each hole boundary point, and determine whether they are false boundary points.

[0095] Further, step 5 classifies the boundary points and window functions, establishes a Bayesian model, and introduces three types of prior knowledge: density, Riemannian manifold, and discrete feature attributes. Maximum likelihood estimation and reconstruction are then performed on the region to be grown to complete the hole repair. Specifically, this includes:

[0096] Step 5.1: Define the set of true values ​​O and the set of measured values ​​M for the target or scene to be reconstructed, where M is generated from O and includes statistical error, and its descriptive model is P(M|O). Generate a... The probability space is denoted by ω, where n is the number of original points, m is the number of measurement points, and ω, ω O ,ω M , and Representing the concept of space.

[0097] Step 5.2: Assuming the measurement process is an unbiased estimation, and describing the measurement process using statistical concepts under Bayes' theorem, the probability that the reconstructed set after a given set of measured values ​​M is exactly the true set O is:

[0098]

[0099] P(M): The probability that the reconstructed set is M; P(O): The probability that the reconstructed set is O; Ω O The interval is estimated using Bayesian estimation.

[0100] Step 5.3: Determine the set O corresponding to the case where P(O|M) is maximized:

[0101]

[0102] Step 5.4: Determine the point cloud obtained during a particular measurement process. In (n>m), each of the m points is mapped to a point in the set of measured values ​​M:

[0103]

[0104] Among them, measurement point m i It is from the original point o i Accompanying probability density p i (o i It is caused by the measurement error of +Δx).

[0105] Step 5.5: The errors in the optical sectioning system are predominantly Gaussian distributed, and the errors are independent of each other. (Reconstruction points...) Conforms to p i (m i -Δx):

[0106]

[0107] Step 5.6: Define the prior set as consisting of three main components: density prior, Riemannian manifold prior, and prior of discrete attribute features, which are independent of each other.

[0108]

[0109] Where Z is a normalization constant representing the integral of all other factors in the set. w(O) is a window function that defines the area to be repaired in the point cloud model and makes the objective function integrable; p density (O) denotes the density prior function of the true value set O, p riemann (O) denotes the Riemannian prior function of the true value set O, p discrete (O) represents the discrete attribute feature prior function of the true value set O.

[0110] The definitions and structures of the three types of prior functions are as follows:

[0111] Density prior function: Ideally (the original point cloud is recorded by a light-cutting system with a known direction of motion, or the point cloud data contains certain marker bits), the expected position of each point in the point cloud is predictable. The sampling space is directly set according to the resolution of the single-frame imaging plane (XOZ plane) of the structured light at a certain moment, making it completely map to the resolution of the imaging device. Then, the number of complete points on the projection plane perpendicular to the direction of motion should be consistent for each frame data in the point cloud model at each sampling interval. Simultaneously, the spatiotemporal intervals of adjacent frames in the third direction of motion (Y-axis) should have strong similarity, i.e., the interval distances tend to be consistent.

[0112] When the actual situation of the point cloud does not directly support such operations, the sampling space is optimized by evaluating the expected distance between adjacent points, thus extending the density theory of semi-ordered point clouds to ordinary point cloud models. A non-equal probability random potential p is defined within the bounded region. dist This indicates that within a proportional neighborhood radius, the probability density has a local maximum at the desired point:

[0113]

[0114] Where, N δ (x) represents the set of all points within radius δ of point x that are contained in set O. Radius δ is calculated iteratively from the expansion region of the hole to be repaired. N can increase positively correlated with the singularity of the original point cloud model, and is generally suitable to be 6.

[0115] Riemannian manifold prior function: Transforms the distribution problem of the original point cloud into an unconstrained optimization problem of the sum of several component functions on a Riemannian manifold.

[0116]

[0117] Here, L is a complete Riemannian manifold, and the function fi is a convex function defined on L. Due to the unidirectionality and closure of the surface to be reconstructed from the point cloud, the incremental subgradient algorithm on the Riemannian manifold must converge on the convex set.

[0118] Meanwhile, this invention defines T p L is the tangent space of manifold L at point p, and TL = ∪ p∈M T p Let L denote the tangent bundle of manifold L, and χ(L) denote the vector field space on L. Then the following derived definition holds:

[0119] (1) Define a T for each p∈L p The inner product g(p) on L = <·,·> p Then g = {<·,·>} p} p∈L ={g(p)} p∈LLet g be a Riemannian metric on a manifold L. Then (L, g) is called a Riemannian manifold, and g ∈ T. 0,2 L is a second-order covariant tensor field.

[0120] (2) Let Let γ:[a,b]→L be a smooth curve in the Riemannian manifold (L,g), and let L be a Levi-Civita connection on the Riemannian manifold (L,g). Let γ be the geodesic curvature vector (or acceleration), where γ′(t) represents the derivative of γ at t. The curve γ is then called a geodesic in L.

[0121] (3) If (L,g) is a smooth Riemannian manifold, given p∈L, v∈T p L, then there exists a unique geodesic γ v [a,b]→L makes γ v (a) = p and γ′ v (a) = v. Where, when γ:[a,b]→L is a geodesic, ‖γ′‖ is a constant; γ is a normal geodesic if and only if ‖γ′‖=1.

[0122] The corresponding incremental subgradient algorithm on the Riemannian manifold is as follows:

[0123] f) Choose any point x0∈L, and let k=0;

[0124] g) Perform an optimization test on the objective function: if Then stop iterating; otherwise, let ψ 0,k =x k If i = 1, proceed to the next step;

[0125] Satisfy α k A sequence of points >0;

[0126] j) Following steps c) and d) above, repeat the calculation until i = m, and then calculate ψ. m,k Let it equal x k+1 ;

[0127] k) Let k = k + 1, then return to step b) to perform the optimization test.

[0128] Discrete attribute prior function: This invention uses an optical sectioning system to acquire raw data and assigns additional discrete attribute labels to each point in the point cloud: determining whether a point belongs to a region (smoothly connected surface), a boundary (boundary line between surfaces), or a corner point (intersection of n ≥ 2 boundaries). We define the following:

[0129] (1) The neighboring region within a certain radius of the discrete feature points mentioned above in the point cloud model is called the special region;

[0130] (2) The point cloud model is divided into independent, uncoupled, smooth regions by each boundary line, and these regions do not contain discrete feature points; these are called ordinary regions. Boundary points belong to two adjacent regions.

[0131] (3) In special regions: the probability of defining a boundary increases with the curvature of the local neighborhood; the probability of defining a corner depends on the number of boundary intersections within the neighborhood;

[0132] (4) Corner points can only exist at the intersection of two or more boundary lines within a certain radius neighborhood, and their probability distribution should satisfy the regression line after each boundary line is optimized to be the same.

[0133] (5) The neighborhood defined in the density prior function and the Riemannian manifold prior function is restricted to the same neighborhood in this process and no additional attributes are added.

[0134] To preserve local details during hole repair, this invention builds the discrete feature optimization process upon prior function estimations. Specifically, when iteratively estimating the probabilities of discrete and continuous attribute assignments, the global continuous estimation results from the first two stages should be used. Considering the contradiction between smoothing effects and edge probability estimation, the influence of the curvature prior penalty term in this process should be set to zero. After optimization convergence, the probabilities of edge points are then assigned to high curvature points.

[0135] The covariance matrix method is used to estimate the normal vectors of each point in the point cloud model, thereby ensuring the correctness of the repaired model. At the same time, in order to avoid changes in prior information caused by sampling conditions, this invention uses geometric definition to determine a set of approximately 20-40 points with a diameter ε, and establishes a local coordinate system within this set using PCA, that is, all points are in a sparse height field in the n direction.

[0136]

[0137] Where, N δ (x) represents the set of all points within radius γ of point x that are contained in set O. γ is typically 3-4 times the average distance (density) between points; G i n is the Gaussian density function; i The normal vector for each target point is estimated by the covariance matrix method; t This is the target point to be estimated.

[0138] This invention transforms the hole repair problem in point cloud models into a maximum likelihood estimation problem based on training samples within a Bayesian framework. Furthermore, it combines the prior information of conditional probability density with the characteristics of the point cloud itself, subdividing it into three prior functions. A local fitting model is then used to approximate the point cloud model, improving the accuracy and confidence of the estimation results.

[0139] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for 3D reconstruction based on semi-ordered point clouds using optical sectioning, characterized in that, include: Step 1: Define the point cloud format as follows: Belongs to point cloud The three-dimensional coordinate information of the point; represent Normal information of a point on the current frame plane; represent Normal information between the point and its two nearest points on the current movement axis; represent Light intensity information of a point; represent The discrete attribute category to which the point belongs; Step 2: Select the target object and scan it to obtain a semi-ordered point cloud; Step 3: Analyze the sources of error in the measurement data; Step 4: Detect and extract hole boundaries in the point cloud model; Step 5: Repair the holes in the point cloud based on the Bayesian probability model; The semi-ordered point cloud is a point cloud with a dimension between that of a discrete point cloud and an ordered point cloud. Step 2 includes: Based on the structured light triangulation method, normal vector information and light intensity information in light stripes are added to the discrete point cloud. When the offset of each cross section layer can satisfy that the vector information covered by the laser stripes of two adjacent frames is not parallel on the current extension line, a spatiotemporal field model can be established in the thickness light stripe. The topological structure information under the preset confidence level can be established in the unified world coordinate system, thereby obtaining the semi-ordered point cloud with a dimension between discrete point cloud and ordered point cloud.

2. The three-dimensional reconstruction method as described in claim 1, characterized in that, The sources of error in step 3 include: random errors introduced by structured light width, collimation, and drift; systematic errors introduced during the construction of the optical cutting system; and random errors introduced by various types of noise in the measurement environment.

3. The three-dimensional reconstruction method as described in claim 2, characterized in that, The optical cutting system is calibrated using a cross-point algorithm.

4. The three-dimensional reconstruction method as described in claim 1, characterized in that, Step 4 includes: Step 4.1: Select a point from the semi-ordered point cloud. Search and generate a neighborhood point set in the point cloud model. ; Step 4.2: Calculate the point Given the covariance matrix, find the eigenvectors corresponding to its smallest eigenvalues ​​and the normal vector of the tangent plane; Step 4.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require Projecting the points onto the unit circle of the tangent plane yields the set of mapped points. ; Step 4.4: Determine the point Is it a point to be determined? Step 4.5: Determine the point based on the prior information in the point cloud model. If a point is a boundary point of a hole, it will be removed if it does not meet the requirements. Step 4.6: Return to Step 4.1 until all points to be determined have been looped; Step 4.7: Verify whether there are other boundary points in the neighborhood of each hole boundary point, and determine whether they are false boundary points.

5. The three-dimensional reconstruction method as described in claim 4, characterized in that, Step 4.4 includes: Calculate the set of mapping points The maximum angle between each inner point and the points on the left and right sides ,make ;like If the value is greater than the judgment threshold, then the point... The point is to be determined; otherwise, the point is... Let be an interior point.

6. The three-dimensional reconstruction method as described in claim 1, characterized in that, Step 5 includes: Step 5.1: Define the set of true values ​​O and the set of measured values ​​M for the target or scene to be reconstructed, wherein the set of measured values ​​M is generated from the set of true values ​​O and includes statistical errors, and its descriptive model is as follows: ; Step 5.2: Assuming the measurement process is an unbiased estimation, and describing the measurement process using statistical concepts under Bayes' theorem, the probability that the reconstructed set after being given the set of measured values ​​M is exactly the true set O is: Step 5.3: Confirm The set O corresponding to the maximization case: Step 5.4: Determine the point cloud obtained during a particular measurement process. In this context, each of the m points is mapped to a point in the set of measured values ​​M. Among them, measurement points It is from the origin point Accompanying probability density This is caused by measurement error; Step 5.5: The errors in the optical sectioning system are predominantly Gaussian distributed, and the errors are independent of each other. (Reconstruction points...) conform to : Step 5.6: Define the prior set as consisting of density priors, Riemannian manifold priors, and discrete attribute feature priors, which are independent of each other. Where Z is a normalization constant, representing the integral of all other factors in the set; It is a window function that defines the area to be repaired in the point cloud model and makes the objective function integrable.

7. The three-dimensional reconstruction method as described in claim 6, characterized in that, The density prior is defined as follows: Define a non-uniform probability random potential within the defined region. This indicates that within a proportional neighborhood radius, the probability density has a local maximum at the desired point: in, Represents the set of all points contained in set O within the radius δ of point x; the radius δ is calculated iteratively from the expansion region of the hole to be repaired; N increases positively correlated with the singularity of the original point cloud model.

8. The three-dimensional reconstruction method as described in claim 6, characterized in that, The Riemannian manifold prior is defined as follows: The problem of the distribution of the original point cloud is transformed into an unconstrained optimization problem of the sum of several component functions on a Riemannian manifold: Here, L is a complete Riemannian manifold, and the function fi is a convex function defined on L; definition Let p be the tangent space of the manifold L. This represents the tangent bundle of the manifold L. Let L represent the vector field space on the manifold L; then the following extended definition applies: (1) For each Define a Inner product Then it is called A Riemannian metric on the manifold L is called It is a Riemannian manifold, and It is a second-order covariant tensor field; (2) Let For the Riemannian manifold Contact Levi-Civita on [website name] It is the Riemannian manifold The smooth curve in, then Called The geodesic curvature vector, where express The derivative at t; if Then it is called a curve. The geodesics in the manifold L; (3) If Given a smooth Riemannian manifold, , Then there exists a unique geodesic. Make and Among them, when When it is a geodesic line, It is a constant; if and only if hour, These are standard geodesic lines; The corresponding incremental subgradient algorithm on the Riemannian manifold is as follows: a) Random point Meanwhile, let k=0; b) Perform an optimization test on the objective function: if If the iteration stops, then stop; otherwise, let... If i=1, proceed to the next step; c) Let Is the component function fi at the point The subgradient at that point, taking the geodesic , making , ;in ; d) Calculation ,Pick , It is for any All satisfied The point sequence; e) Repeat steps c) and d) above until... In this case, please obtain Make it equal to ; make Return to step b) to perform an optimization check.

9. The three-dimensional reconstruction method as described in claim 6, characterized in that, The prior definition of the discrete attribute features is: Determine whether a point belongs to the type of region, boundary, or corner point, where the region is defined as a smoothly connected surface, the boundary is defined as the boundary line between surfaces, and the corner point is defined as the intersection of n ≥ 2 boundaries; where... (1) The point cloud model includes a neighboring region within a certain radius, including the discrete feature points mentioned above, which is called a special region; (2) The point cloud model is divided into independent and uncoupled smooth regions by each boundary line, and the region does not contain discrete feature points, which is called a normal region; the boundary points belong to two adjacent regions. (3) In the special region: the probability of the boundary increases with the curvature of the local neighborhood; the probability of the corner point depends on the number of boundary intersections in the neighborhood; (4) The corner point can only exist at the intersection of two or more boundary lines within a certain radius neighborhood, and its probability distribution should satisfy the regression line after each boundary line is optimized to be the same; (5) The neighborhood defined in the density prior and the Riemannian manifold prior is restricted to the same neighborhood in this process and no additional attributes are divided.

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